<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Daudin's Milk Composition Data</title>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<link rel="stylesheet" type="text/css" href="R.css" />
</head><body>

<table width="100%" summary="page for milk"><tr><td>milk</td><td style="text-align: right;">R Documentation</td></tr></table>

<h2>Daudin's Milk Composition Data</h2>

<h3>Description</h3>

<p>Daudin et al.(1988) give 8 readings on the composition of 86
containers of milk.  They speak about 85 observations, but this
can be explained with the fact that observations 63 and 64 are
identical (as noted by Rocke (1996)).
</p>
<p>The data set was used for analysing the stability of principal
component analysis by the bootstrap method.  In the same context, but
using high breakdown point robust PCA, these data were analysed by
Todorov et al. (1994).  Atkinson (1994) used these data for ilustration
of the forward search algorithm for identifying of multiple outliers.
</p>


<h3>Usage</h3>

<pre>data(milk, package="robustbase")</pre>


<h3>Format</h3>

<p>A data frame with 86 observations on the following 8 variables, all
but the first measure units in <em>grams / liter</em>.
</p>

<dl>
<dt><code>X1</code></dt><dd><p>density</p>
</dd>
<dt><code>X2</code></dt><dd><p>fat content</p>
</dd>
<dt><code>X3</code></dt><dd><p>protein content</p>
</dd>
<dt><code>X4</code></dt><dd><p>casein content</p>
</dd>
<dt><code>X5</code></dt><dd><p>cheese dry substance measured in the factory</p>
</dd>
<dt><code>X6</code></dt><dd><p>cheese dry substance measured in the laboratory</p>
</dd>
<dt><code>X7</code></dt><dd><p>milk dry substance</p>
</dd>
<dt><code>X8</code></dt><dd><p>cheese product</p>
</dd>
</dl>



<h3>Source</h3>

<p>Daudin, J.J. Duby, C. and Trecourt, P. (1988)
Stability of Principal Component Analysis Studied by the Bootstrap Method;
<em>Statistics</em> <b>19</b>, 241&ndash;258.
</p>


<h3>References</h3>

<p>Todorov, V., Neyko, N., Neytchev, P. (1994)
Stability of High Breakdown Point Robust PCA,
in <em>Short Communications, COMPSTAT'94</em>; Physica Verlag, Heidelberg.
</p>
<p>Atkinson, A.C. (1994)
Fast Very Robust Methods for the Detection of Multiple Outliers.
<em>J. Amer. Statist. Assoc.</em> <b>89</b> 1329&ndash;1339.
</p>
<p>Rocke, D. M. and Woodruff, D. L. (1996)
Identification of Outliers in Multivariate Data;
<em>J. Amer. Statist. Assoc.</em> <b>91</b> (435), 1047&ndash;1061.
</p>


<h3>Examples</h3>

<pre>
data(milk)
(c.milk &lt;- covMcd(milk))
summarizeRobWeights(c.milk $ mcd.wt)# 19..20 outliers
umilk &lt;- unique(milk) # dropping obs.64 (== obs.63)
summary(cumilk &lt;- covMcd(umilk, nsamp = "deterministic")) # 20 outliers

</pre>


</body></html>
